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We investigate the maximization of the received power from compact multiple antenna systems in random RF fields, using two novel impedance matching approaches. The first approach is based on optimal impedance matching where we use convex optimization to propose a sparse optimal impedance matching technique. The second approach is obtained by further relaxing the sparse optimal impedance matching method to obtain a suboptimal impedance matching (SOM) method we refer to as multiport ladder matching (MLM). Simulation results show that the sparse optimal impedance matching approach provides the maximum received power while MLM can capture more power than conventional single-port matching (SPM). Additionally, they can maintain good bandwidth indicating the effectiveness of the sparse optimal and multiport ladder impedance matching approaches.